**Table of Contents**show

## Introduction

Whenever there is a question that has an answer in yes/no, true/false, or we have to choose one out of many options, we immediately tend to make a decision. For example, “Do you want milk now?”, “Should I take up this course or that?” etc. A computer can do that too – provided we train it using some algorithms. Decision tree in machine learning is used extensively to solve these types of problems. Decision trees can be used for both classification and regression problems.

### Classification algorithms

Classification algorithms help us categorize data into distinct classes so that we can assign a label to each class. Classification algorithms are widely used for handwriting recognition, speech recognition, biometric identification, etc… There are two types of classifiers –

- Binary classifier – these classifiers have only 2 distinct outcomes (classes). For example, whether an email is a spam or not, whether a person is male or female, whether a student passes or fails.
- Multi-class classifier – classifiers having more than 2 classes or outcomes. Example, colours of various objects, classification of different songs based on moods, etc…

Let us take a simple dataset to show a classification problem –

Shape |
Colour |
Vegetable |

Round | Green | Cabbage |

Oval | Green | Cucumber |

Oval | Orange | Carrot |

Oval | Purple | Brinjal |

Round | Yellow | Squash |

Oval | Yellow | Potato |

Round | Red | Tomato |

The shape and colour are called attributes of the dataset and the vegetable is the label. For example, if the input is oval and green, then the answer will be cucumber as per the dataset. Now, if a new input is given with the attribute oval and yellow, a decision tree can ask questions like is the shape oval or is the colour yellow, and accordingly, label it as Potato.

### Decision Tree in machine learning

The decision tree in machine learning is an important and accurate classification algorithm where a tree-like structure is created with questions related to the data set. The answer to each question leads to another question, which leads to another, and so on until we reach a point where no more questions can be asked. How the questions are asked and what attributes are chosen is decided based on some calculations which we will discuss in this article later. A simple decision tree in the machine learning world looks like –

This is a simple tree where a student can decide which subject he can take up based on the marks. Thus, ‘marks’ is the main attribute here, and we decide the questions to be asked based on this attribute.

The decision tree is easy to understand and can be represented in a diagrammatic manner making it easy to visualize. It can handle quantitative as well as categorical data. It is widely used for predictive data analysis.

But how do you decide what questions to ask?

To answer this, let us create a decision tree for the above classification dataset that we have.

The next question will be based on the answer to this question. Thus, the questions are based on the attributes of the dataset.

How do you decide which should be the best attribute?

This is where our machine learning algorithms come into the picture. We decide the attribute based on how well the decision tree can be split and unmixed using the attribute. Before getting into details of this, let us understand the types of decision tree algorithms and important terms associated with decision trees in machine learning.

### Types of decision tree algorithms

We can create a decision tree using many different algorithms. The most popular algorithms are –

- ID3 (Iterative Dichotomiser 3) – ID3 algorithm iterates through each attribute of the dataset to find the
*entropy*and*Information Gain*of the attribute. The attribute with the highest Information gain is then taken as the root node that splits the decision tree. - CART (Classification And Regression Tree) – This algorithm can be used for classification (category) as well as regression (numeric) problems. It is a binary decision tree where the root node is split into two child nodes by asking a set of questions. The questions should resemble the dataset. The answer to each question further splits the node and the next question can be asked.
- Chi-square automatic interaction detection (CHAID) – This decision tree technique is used for the detection of interaction between 2 or more variables, classification, and prediction. It is mostly used for targeted marketing to certain groups and predicts how they respond to different scenarios.

We mentioned entropy and information gain…

What are they?

In this article, we will create a decision tree from scratch and understand the terminologies associated with it. But, first, let us familiarize ourselves with the important terms that we will be using in constructing our decision tree.

### Important terms

Some important terms used in the decision tree algorithm are –

- Gini Index – Gini index is an index used to quantify the amount of uncertainty.
- Entropy – The measure of impurity in the dataset. If all the labels and items are the same, the impurity is zero. For example,

However, if there are mixed items in the dataset, the probability of the label and item being the same becomes less. Such a dataset will have an impurity value as non-zero.

This means that if the degree of randomness in the data is high, impurity ≠ 0.

However, if data is pure or impure (i.e. no randomness), impurity and thus entropy are both zero.

Suppose we split our decision tree based on a question, is the ball Orange? There could be two answers – yes or no. In a dataset with 100 such rows, there could be many orange balls and balls of other colours. Suppose there are 50 orange balls and 50 others. Then, there would be 50 yes and 50 no as answers for the question. In a situation like this,

where n(yes) = n(no), entropy will always be = 1.

In general, the entropy of a sample S in a dataset can be calculated as –

Entropy(S) = -P(yes)log2P(yes) – P(no)log2P(no) |

- Information Gain – This value decides which attribute should be selected as the main decision node based on how much information it gives to us. We measure the reduction in entropy for the sample S to get the information gain –

Information gain = Entropy(S) – Information Taken, where “information taken” is calculated as {Weighted average x Entropy (individual features)}

Thus,

Information gain = Entropy(S) – {Weighted average x Entropy (individual features)} |

- Chi-Square – It is used to find the importance of the difference between the parent node and subnodes
- Variance reduction – It is used for regression problems (continuous variables) where split with lower variance acts as the criteria for splitting the sample.

Some important terms related to the decision tree diagram are –

- Root node – It is the first node of the decision tree, the point where the tree starts. It represents the entire sample.
- Leaf node – It is the last node of the decision tree. After this, no more segregations are possible.
- Subtree/branch – When we split the node or tree, we get these.

- Splitting – Dividing the nodes into subparts, based on a question or condition
- Pruning – Removing the unnecessary, excess, or unwanted nodes of the tree. Pruning helps in avoiding overfitting
- Parent/Child – Except for the root node, all the nodes of a decision are called child nodes. Some nodes can be both parent and child when there are multiple branches. The root is always the parent node.

Try these examples to create decision trees and understand each part of the diagram.

- A person will buy a certain product during shopping
- A person will diagnose positive for a heart disease
- Check if an email is spam or not

### Building a decision tree in Machine learning

We know how to create a tree and split the nodes – but one question remains unanswered –

“*How to decide the best attribute?”*

We will focus on answering this question by using the following data set. In the below dataset, 3 attributes will be used to answer the question, *“Should I eat a banana today?”*

Yes, you are right! That’s a simple problem for our brain – but how does the computer do it?

State of the banana |
Health of the person |
Weather |
Eat or not? |

Raw | Good | Sunny | No |

Ripe | Cough | Rainy | No |

Ripe | Wheezing | Sunny | No |

Ripe | Cough | Sunny | Yes |

Ripe | Wheezing | Rainy | No |

Ripe | Good | Rainy | Yes |

Ripe | Good | Sunny | Yes |

Raw | Good | Rainy | No |

Take some time to understand the dataset.

If the banana is ripe, but the person who wants to have it has wheezing, he/she should not eat it.

If the banana is ripe, the person who wants to have it has a cough, but if the weather is sunny, he/she can eat it.

Same way, others.

There are 8 instances in our ‘Banana’ dataset. There are 5 No values and 3 Yes values. This means the probability of getting No as the answer is 5/8 and Yes is 3/8.

Remember Entropy? Let’s calculate that using the formula we mentioned above –

Entropy E(S) = -(3/8)*log2(3/8) – (5/8)*log2(5/8)

= -3/8*(-1.415)-5/8*(-0.678)

= **0.95**

If we had had an equal number of Yes and No, remember the entropy would have been —??

Yes, it would be 1.

We have three attributes, state, health, and weather. Which attribute should be our root node? To decide this, we need to know the information gain that each attribute can give us. Whichever node gives the maximum information gain wins!

How do we calculate information gain? Let us do it using the formula we mentioned above!

The above formula should be applied to each attribute to calculate the information gain.

*Attribute 1 – State*

To calculate information gain, we need to first calculate information taken, which is again calculated by multiplying the weighted average with the entropy of individual features values. In this case, the values are ripe and raw.

For a totally impure or pure set (no randomness), the entropy is 0 as we have seen before.

Therefore, Entropy (Raw) = 0 because there is no yes, only no. If we calculate this using the formula, we will get the same result.

Entropy (Ripe) = 1 because of the equal number of yes and no. Using the formula, we can calculate this as -(3/6)*log2(3/6)-(3/6)*log2(3/6) = 1.

Information taken, IT(State) = 2/8*Entropy(Raw) + 6/8*Entropy(Ripe) = 2/8*0 + 6/8*1 = 0.75

Information gain, IG(State) = E(S) – IT(State) = 0.95-0.75 = **0.20**

Now, let’s calculate the same for the next attribute i.e. health –

E(Health = Good) = 1 (Guess, why?)

E(Health = Cough) = 1

E(Health = Wheezing) = 0

Information Taken, IT(Health) = 4/8*1 + 2/8*1 + 2/8*1 = 0.75

IG(Health) = 0.95 – 0.75 = **0.20**

The last attribute is Weather, so let us calculate the IG with that –

E(Sunny) = 1

E(Rainy) = -1/4*log2(1/4) – ¾*log2(3/4)

= 0.5 + 0.31125 = 0.81125

Information Taken, IT(Weather) = 4/8*1 + 4/8*0.81125 = 0.905625 = 0.90

Information Gained, IG(Weather) = 0.95 – 0.90 = **0.05**

When we compare the 3 values, we note that IG(Health) and IG(State) have better information gain as compared to IG(Weather). Since both IG(Health) and IG(State) are equal, we can use any of them as the root node to create the decision tree. We are taking the Health attribute. This is how our decision tree should look like –

The last nodes with the yes and no values are the leaf nodes because the decision tree ends there.

One last thing on this decision tree and then we will move on to how the computer internally performs the logic of getting the yes and no.

Pruning the tree!

We can prune this tree by removing all the no values so that we get a compact tree.

We can represent this using Boolean values, for example, if health is good AND state is ripe, we can eat the banana. Same way, if we have a cough but the weather is sunny, we can eat. However, if you have a cough OR weather is rainy, we cannot eat the banana. This means we can represent decision trees in machine learning using OR, AND, NOT, and XOR operators.

AND

A |
B |
A AND B |

F | F | F |

F | T | F |

T | F | F |

T | T | T |

OR

A |
B |
A OR B |

F | F | F |

F | T | T |

T | F | T |

T | T | T |

XOR

A |
B |
A XOR B |

F | F | F |

F | T | T |

T | F | T |

T | T | F |

In the above case, we have only two attributes A & B. If we have more attributes, like C, D, E, and so on, the tree will need an exponential number of nodes. For n attributes, the number of nodes will be approximately 2^n or 2n.

This is all how to create a perfect decision tree in machine learning.

The above table is called a truth table.

### Decision Tree Boundary

The goal of a decision tree in machine learning is to create a boundary that separates the data into linear, rectangular, or hyperplane based on the qualities of the data. The decision boundary forms as each data point settle into space in the X-Y coordinates. Let’s take a simple example –

Suppose there are some numbers in a dataset {10, 12, 15, 16, 27, 56, 67, 45, 89, 34, 76, 95, 23, 90}

Consider each of the numbers as a data point. When we get a new number, say, 65, where should it go? Our decision tree asks the question – is the number greater than 50?

The new number 65 thus goes to the red group where all the numbers greater than 50 are placed. The dashed line is the boundary that is created when the decision tree splits the data. If there are more variables, the plane will change accordingly.

#### When to use decision trees in machine learning

We can use decision trees when –

- We need an algorithm that can be easily viewed and represented
- High nonlinearity
- Define a complex relation between independent and non-independent variables.

### Python code implementation of a decision tree in machine learning

To build a decision tree in machine learning using Python, we use the scikit-learn library. Let us import the required libraries to start with.

#Importing libraries import pandas as pd import numpy as np from sklearn.tree import DecisionTreeClassifier from sklearn.model_selection import train_test_split

The next step is to get the data. We can create the data, or load it from the existing datasets.

training_data = [[‘Round’, ‘Green’], [‘Oval’, ‘Green’], [‘Oval’, ‘Orange’], [‘Oval’, ‘Purple’], [‘Round’, ‘Yellow’], [‘Oval’, ‘Yellow’], [‘Round’, ‘Red’]] label_data = [‘Cabbage’, ‘Cucumber’, ‘Carrot’, ‘Brinjal’, ‘Squash’, ‘Potato’, ‘Tomato’]

We have fewer data in our dataset. However, you can expand to add more rows or use an existing dataset that comes with sklearn.

Let’s split the data into training and testing sets.

X_train, X_test, y_train, y_test = train_test_split(training_data, label_data, random_state = 47, test_size = 0.25)

To find the information gain, we need to find the entropy, which will be the criteria for splitting the decision tree, as we saw earlier in our banana example. For this, we will need to get the DecisionTreeClassifier from sklearn library (we have already imported it).

data_classifier = DecisionTreeClassifier(criterion = 'entropy')

To get more accuracy, we can set the minimum number of samples along with the criterion as min_samples_split = n, where n will be the minimum number of data samples required to split the node. We can do this if the accuracy of the training data is more than the accuracy of the test data.

Next, we use the classifier to train the data –

data_classifier.fit(X_train, y_train)

Now, we use the algorithm to predict test data. We will have to import the accuracy metric from the sklearn.metrics library –

y_pred = data_classifier.predict(X_test) from sklearn.metrics import accuracy_score print('accuracy score - training data: ', accuracy_score(y_true=y_train, y_pred=data_classifier.predict(X_train))) print('accuracy score - test data: ', accuracy_score(y_true=y_test, y_pred=y_pred))

## Conclusion

We have covered the basics of a decision tree in machine learning and how to create one from scratch taking a simple example. You can try doing the same for the other examples we have mentioned in our article. The decision tree is the most appealing algorithm for visualizing what is happening at each step and can handle categorical as well as numeric data. Decision trees are resistant to outliers and require very little pre-processing. However, they are prone to overfitting and can create a high bias if some classes are more dominant. Using decision trees, we can establish and understand complex relationships between dependent and independent variables as well.

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